Admissible congruences on type B semigroups

Abstract

Abstract The main aim of this article is to study admissible congruences on a type B semigroup. First, we give characterizations of the minimum admissible congruence whose trace is a normal congruence on a type B semigroup. After obtaining some properties of admissible congruences with the same trace on a type B semigroup, we introduce the notion of a normal subsemigroup and give characterizations of the minimum and maximum admissible congruences whose kernels are normal subsemigroups. Finally, the concept of a congruence pair of a type B semigroup is given, and two congruences associated with the congruence pair are obtained.